ERIC EJ776882: A Unit Price Evaluation of Severe Problem Behavior

2007·0.18 MB·English

by  ERIC

JOURNALOFAPPLIEDBEHAVIORANALYSIS 2007, 40, 463–474 NUMBER3 (FALL2007)
A UNIT PRICE EVALUATION OF
SEVERE PROBLEM BEHAVIOR
JOHN C. BORRERO, MONICA T. FRANCISCO, ALAYNA T. HABERLIN,
NOE¨L A. ROSS, AND SANDEEP K. SRAN
UNIVERSITYOFTHEPACIFIC
Weevaluatedproblembehaviorexhibitedby6individualswithdevelopmentaldisabilitiesusing
the behavioral economic conceptualization of unit price. Descriptive observations were
conducted during interactions between the participants and their primary care providers in
a clinical laboratory, the participants’ homes, or school. Data were recorded on potential
reinforcers and problem behavior. After identifying reinforcers for each participant’s problem
behaviorbywayoffunctionalanalysis,thedescriptivedatawereanalyzedretrospectively,using
the cost–benefit ratiodescribed by theconcept of unit price. Results showed thatdemand was
elasticandproducedmonotonicresponseoutputcurves.Theresultsrepresentanextensionofthe
concept of unit price to severe problem behavior under naturally occurring environmental
conditions.
DESCRIPTORS: unit price, behavioral economics, descriptive analysis, severe problem
behavior,functional analysis
_______________________________________________________________________________
Behavioral economics is an area within behavioral economic conceptualizations of con-
behavior analysis in which responses are viewed sumption were suggested by Kagel and Winkler
as analogous to one’s income, and reinforcers (1972), particularly for the design and evalua-
are viewed as analogous to commodities avail- tion of the familiar token economy or token
able for purchase (Hursh, 1980, 1984). As system (e.g., Phillips, Phillips, Fixen, & Wolf,
defined by Madden (2000), behavioral econom- 1971). More recently, behavioral economic
ics involves the combination of microeconomic approaches have been applied to evaluate
concepts, principles, and measures, as well as response allocation, in applied contexts, under
behavior-analytic methods and principles. This open and closed economies (Roane, Call, &
amalgamation has yielded a fruitful body of Falcomata, 2005), response allocation under
experimental research (see, e.g., the November, increasing effort requirements (e.g., Perry &
1995, special issue on behavioral economics in Fisher, 2001), and reinforcer demand under
the Journal of the Experimental Analysis of increasing price requirements (e.g., Kerwin,
Behavior). The implications for application of Ahearn,Eicher,&Burd,1995;Roane,Lerman,
& Vorndran, 2001; Tustin, 1994), to name
We thank Jori Andrus, Jamie Bartels, Daniela Gutier- only a few applications. The current investiga-
rez,JoleneSy,andAmyWilliamsfortheirassistancewith
tion focuses on evaluations of spending (prob-
data analysis. We also thank Carrie Borrero and Jorge
Reyes for their conceptual contributions to this project. lem behavior exhibited by individuals with
Finally, we are extremely grateful for the instructive developmental disabilities) and consumption
commentsprovidedbyKenSilvermanandtheanonymous
(of reinforcers for problem behavior identified
review panel. Portions of this research were presented at
the 24th meeting of the California Association for via functional analysis) under naturally occur-
BehaviorAnalysisinBurlingameandatthe32ndmeeting ring price, or response requirement, increases.
of the Association for Behavior Analysis in Atlanta,
Behavioral economic analyses focus attention
Georgia.
DirectcorrespondencetoJohnC.Borrero,whoisnow on two measures: consumption (how much of
attheDepartmentofPsychology,UniversityofMaryland the reinforcer is obtained) and spending (how
Baltimore County, 1000 Hilltop Circle, Baltimore,
much responding, or currency, is allocated to
Maryland21250(e-mail: [email protected]).
doi:10.1901/jaba.2007.40-463 obtain the reinforcer; Madden, 2000). When
463
464 JOHN C. BORRERO et al.
combined, these measures produce a cost– increasedfrom$1.00perkilogramto$2.00per
benefit ratio made up of the number of kilogram, this would represent a 50% increase
responses emitted per reinforcer (i.e., unit price; in price. To characterize demand for tomatoes
e.g., Foster & Hackenberg, 2004). Alternative- as elastic, consumption would necessarily de-
ly, stated in economic terms, unit price is the crease by more than 50% (i.e., a demand curve
amount of income expended to access a com- with slope between 21 and 2‘). Inelastic
modity. For example, if a 1-l bottle of juice demand describes a subproportional change in
costs $4.00 and the 2-l bottle of the same juice consumption as a function of changes in price.
costs $5.50, the price per unit (i.e., liter) is Thus, in the tomato example, if the price of
cheaperforthelargerbottle(i.e.,$4.00perliter tomatoes increased from $1.00 per kilogram to
vs. $2.75 per liter). Basic and applied research $2.00 per kilogram and consumption of
on reinforcement parameters (e.g., rate, quality, tomatoes decreased by a mere 25%, then
delay,effort)hasshownthatthesevariablesmay consumption for tomatoes would be character-
interact to influence overall consumption (e.g., izedasinelastic(i.e.,ademandcurvewithslope
Hursh, Raslear, Shurtleff, Bauman, & Sim- between 0 and 21). Frequently, experimental
mons, 1988; Neef, Shade, & Miller, 1994). behavioral economic research has shown that
Thus, conceptualizations of unit price can also the left portions of consumption and spending
be arranged to accommodate variables other curves illustrate inelastic demand (subpropor-
than reinforcers per response. For example, the tional changes in consumption), and the right
juice choice may be influenced by the effort portionsofbothcurvesillustrateelasticdemand
associated with obtaining the larger bottle (e.g., (superproportionalchangesinconsumption).In
reaching to a higher shelf), the delay associated other words, under initial price increases,
with obtaining the larger bottle (e.g., waiting spending increases such that a similar level of
forthestockperson torefill theshelves),and so the commodity is produced. However, when
on. increases in price reach a critical value (termed
The behavioral economic concepts of con- P ; Hursh, 2000), consumption shifts from
max
sumption,spending,andunitpricemaybeused inelastic to elastic.
to quantify demand and demand elasticity. The extent to which the slope of the demand
Demand refers to the function relating the function changes from one unit price to the
amount of the commodity consumed to the next describes the type of demand (e.g., elastic
prevailing price for each unit of the commodity or inelastic; Allison, 1983), because as noted by
(Hursh, 1980). The effects of changes in price Hursh (1980), demand curves tend to slope
(on consumption) are predicted to follow the downward, thus producing a slope less than
economic law of demand, which states that, zero. Therefore, demand curves can be used as
with all other things being equal, consumption a means to assess stimulus value, in that flatter
of a commodity (reinforcer) decreases as its functions suggest higher value stimuli because
price increases (Chaloupka & Pacula, 2000). consumption changes little as price increases.
Demand elasticity is the extent to which Further, if a stimulus is highly valued and the
consumption of a commodity is influenced by demand curve is flat, response output would be
alterations in price for that commodity (Green expected to increase dramatically with increas-
& Freed, 1993). Further, demand elasticity can ing price in order to maintain the level of
be broadly characterized as elastic or inelastic. consumption observed at lower unit price
Elastic demand describes a superproportional values.
changeinconsumptionasafunctionofchanges Tustin (1994) evaluated demand functions
in price. For example, if the price of tomatoes obtained from 3 individuals with developmen-
UNIT PRICE AND SEVERE PROBLEM BEHAVIOR 465
tal disabilities using qualitatively different ioral economic concepts. Similarly, conceptua-
stimuli (e.g., auditory, visual) and button lizations of a variety of a problematic responses
pressing as the operant. Participants were (e.g., severe problem behavior, substance abuse)
exposed to a concurrent-schedules arrangement as consumer demand allow analyses informed
in which one stimulus (e.g., a visual stimulus) by economic concepts known to influence
couldbeobtainedforaconstantprice(e.g.,five consumer demand, for example, unit price
responses produced one reinforcer, Unit Price (Madden, 2000). However, the extent to which
5), and the second stimulus (e.g., an auditory economic concepts, in particular the concept of
stimulus) could be obtained under increasing unit price, are of utility in nonexperimental
schedule requirements. For example, while the (descriptive) contexts, at the level of the
visual stimulus could be obtained for five individual, has been the subject of appreciably
responses, auditory stimuli were evaluated un- less behavior-analytic research (see Oliveira-
der fixed-ratio schedules of 1, 2, 5, 10, and 20. Castro, Foxall, & Schrezenmaier, 2006, for
Characteristic decreases in consumption were a recent notable exception). Clearly, economic
obtained across increasing prices for one of the theory is rooted in the prediction of consumer
concurrently available stimuli. An apparent behavior under relatively uncontrolled contexts.
preference reversal was also observed in that Classic economics does not control price and
a stimulus initially preferred at relatively low observe changes in consumption; rather econ-
prices (i.e., response requirements) was relative- omists observe natural variations in price and
lylesspreferredwhenthepriceforthatstimulus then relate them to variations in consumption.
increased. For example, a change in the price of gasoline
More recently, Madden, Bickel, and Jacobs servesas an appropriateindependent variableto
(2000) tested three predictions of unit price measure an array of dependent variables (e.g.,
using chronic smokers as participants and gas consumption, spending, the use of public
cigarette puffs as reinforcers. Most germane to transportation as an alternative form of re-
the current study was the prediction that inforcement). However, such evaluations typi-
increases in the price per puff would produce cally assess the behavior of large groups (e.g.,
decreases in overall consumption (reinforcers residents of a particular region in the United
obtained) and spending (response output) States).
would produce a bitonic function with in- The purpose of the present study was to
creasing prices, both on double logarithmic assess the concept of unit price using the
coordinates. Participants were required to pull conceptual orientation employed by J. C.
plungersaccording to apredetermined schedule Borrero and Vollmer (2002). Borrero and
to produce cigarette puffs, and unit price was Vollmer conducted descriptive observations of
systematically altered. Consistent with prior caregiver–participant interactions and recorded
research, decreases in consumption were ob- instances of problem behavior, appropriate
served under increasing price requirements. behavior, and various environmental events
Hursh (1984) suggested that the utility of (e.g., periods of low attention). Next, the
economic concepts rests in part on the validity researchers conducted functional analyses to
of findings obtained in laboratorycontexts with identify reinforcers for problem behavior, and
individuals (and not large-group evaluations). then retrospectively evaluated relative response
This is clearly a position espoused by behavior and reinforcer rates using the strict (Herrnstein,
analysts and is evidenced by the relatively large 1961) and generalized (Baum, 1974) matching
basic experimental and growing applied exper- equations. The experimental demonstration of
imental literature testing the utility of behav- reinforcers for problem behavior was important
466 JOHN C. BORRERO et al.
in that interpretations of the data via the a 9-year-old boy who had been diagnosed with
matching equations could be related to those moderate mental retardation and fetal alcohol
from basic and applied experimental work in syndrome. His problem behavior consisted of
which reinforcers are known and not assumed. aggression (e.g., hitting and kicking others).
In the current study, the same sequence of Walsh was a 7-year-old boy who had been
eventswasfollowed,includingtheexperimental diagnosed with mild mental retardation and
identification of reinforcers for problem behav- a seizure disorder. His problem behavior
ior, and evaluated levels of response output consisted of aggression and disruption. Antoine
(problem behavior), given changes in the price was an 8-year-old boy who had been diagnosed
of events shown to reinforce problem behavior. with autism and moderate mental retardation.
The purpose of the current study was to assess His problem behavior consisted of aggression
work and demand functions under naturally and disruption.
occurring increasing price values at the level of
Sequence of Events
the individual and at the level of a group of 6
Descriptive analysis and settings. Descriptive
participants.
data were gathered for each participant using
methods described by Vollmer, Borrero,
METHOD
Wright, Van Camp, and Lalli (2001). Ob-
Participants servers used a computerized data-collection
Six individuals participated in various por- system to record three potential reinforcers
tions of this study.1 Mandy was a 24-year-old (instruction termination, access to tangible
woman who had been diagnosed with Sticklers items, and attention) and problem behavior
syndrome and mild mental retardation. Her (individually defined for each participant). The
problem behavior consisted primarily of self- term potential reinforcer was used to describe
injurious behavior (SIB) including head bang- events that occurred subsequent to problem
ing, nose punching, chin punching, and head behavior because at the time of the descriptive
hitting. Bruno was an 11-year-old boy who had observations, functional analyses had not been
been diagnosed with autism. His problem conducted for any participant (thus, functional
behavior consisted of aggression, disruptive reinforcers were not known). Descriptive anal-
behavior (e.g., throwing academic materials), yses were conducted before functional analyses
and SIB (head and face hitting). Dan was a 9- to capture behavior in the natural environment
year-old boy who had been diagnosed with prior to exposure to experimental contingencies
in the functional analysis. Attention was defined
moderate mental retardation and cerebral palsy.
as physical or verbal interaction between the
His problem behavior consisted of aggression
participant and his or her primary care pro-
(e.g., hitting and kicking others) and disruptive
viders. Instruction termination was defined as
behavior (e.g., throwing materials). Todd was
removal of demands and instructional materials
for a period of at least 3 s, or the absence of
1DescriptivedataforMandyandToddwerepreviously
reported in Vollmer, Borrero, Wright, Van Camp, and instructions if the participant disengaged from
Lalli(2001)asprobabilityvalues.Functionalanalysisdata a previously specified task for at least 3 s. Access
for Todd were previously reported in Vollmer, Borrero,
to tangible items was defined as availability of
Lalli, and Daniel (1999). Descriptive and functional
previously restricted items for manipulation.
analysisdataforMandyandDanwerepreviouslyreported
in J. C. Borrero and Vollmer (2002). Descriptive and Potential reinforcers and potential establishing
functional analysis data for Walsh and Antoine were operations were recorded as duration measures,
previouslyreportedinC.S.W.Borrero,Vollmer,Borrero,
and instances of problem behavior were re-
and Bourret (2005). However, data reported for these
participants werenever evaluatedin terms ofunit price. corded as a frequency measure.
UNIT PRICE AND SEVERE PROBLEM BEHAVIOR 467
Descriptive observations for Mandy, Todd, imately twice per minute. Instances of problem
and Walsh were conducted on an inpatient behavior resulted in a 30-s break from the
hospital unit during interactions with their instructional sequence. In the absence of
primary care providers. The inpatient hospital problem behavior, the instructional sequence
facility was furnished with a couch, chairs, continued. The escape condition was designed
tables,andatelevision.Descriptiveobservations to test for behavioral sensitivity to escape from
for Dan and Antoine were conducted in their instructions as reinforcement.
homes, throughout various rooms of the house, An alone condition (Mandy) and a no-
during interactions with their biological parents consequence condition (Bruno) were also in-
andsiblings (forDan). Descriptiveobservations cluded. In the alone condition, the participant
for Bruno were conducted in his classroom was escorted into a room with no tangible
during regularly scheduled activities with his materials provided, and no programmed con-
classroom teachers. tingencies were in place for SIB. The no-
Functional analysis. The problem behavior of consequence condition was similar to the alone
each participant was exposed to functional conditioninthatnoprogrammedcontingencies
analysis using procedures similar to those were arranged for problem behavior and no
described by Iwata, Dorsey, Slifer, Bauman, tangible items were provided. However, due to
and Richman (1982/1994). Trained clinical the arrangement of the setting (his classroom),
therapists or trained graduate students con- Bruno was not alone during these sessions. The
ducted all functional analyses. Four test condi- alone and no-consequence conditions were
designed to evaluate response persistence in
tionsand acontrolcondition were alternatedin
the absence of programmed social contingen-
a multielement design.
cies.
In the attention condition, the participant
Eachtestconditionwascomparedtoacontrol
had access to a task or activity but did not have
condition in which no programmed contingen-
access to attention in the absence of problem
cies were arranged for problem behavior, no
behavior. Instances of problem behavior re-
instructional demands were delivered, and
sultedin30 sofattentionfromthetherapist(in
therapist attention and preferred tangible items
the form of statements of concern). The
were freely available (on a continuous or nearly
attention condition was designed to test
continuous schedule). Functional analyses
behavioral sensitivity to adult attention as
were either 5 min (Bruno and Antoine) or
a reinforcer.
10 min (Mandy, Dan, Todd, and Walsh) in
Duringthetangiblecondition,theparticipant
duration.
received brief access to a preferred tangible item
(or food item for Todd) that was subsequently
Interobserver Agreement
restricted and returned contingent on problem
Interobserver agreement was assessed by
behavior.Givenaninstanceofproblembehavior,
having a second observer simultaneously but
theparticipantreceivedaccesstotheitemfor30 s
independently record data on problem behav-
(or a bite of food). Attention was delivered
ior, potential establishing operations (e.g., low
throughout tangible conditions, irrespective of attention), and potential reinforcers (e.g.,
problem behavior (on a continuous or nearly attention). Agreement was calculated using
continuousschedule).Thetangibleconditionwas partial agreement within intervals (e.g., Iwata,
designed to test behavioral sensitivity to tangible Pace, Cowdery, & Miltenberger, 1994). Each
items as reinforcement. observation was divided into 10-s intervals, and
In the escape condition, the participant agreement between both observers was assessed
received instructions to complete tasks approx- across each interval. The smaller number (in
468 JOHN C. BORRERO et al.
each 10-s interval) was divided by the larger participant. Given the partitioning of the
number, and all values were averaged for the descriptive observations, each participant’s data
entire observation. Interobserver agreement was yielded three unit price values. Once parti-
assessed during 37% of all descriptive observa- tioned, we calculated the total number of
tions. Interobserver agreement data for re- reinforcers delivered and the instances of
inforcers are reported for relevant conditions problem behavior emitted during each equal
only (i.e., those conditions shown to reinforce interval. The unit price for each interval was
problem behavior, as demonstrated via func- then calculated by dividing the total number of
tional analysis). For Mandy, agreement aver- responses emitted by the total number of
aged 84% for attention, 100% for access to reinforcers obtained. An event counted as
tangible items, and 84% for problem behavior. a reinforcer if (a) it was an event identified via
For Bruno, agreement was 87% for escape functional analysis as a reinforcer, and (b) the
from instructional demands (range, 80% to event was available within 10 s of problem
99%), 98% for access to tangible items (range, behavior.Theuseof10-swindowwasbasedon
97% to 98%), and 100% for problem prior work (C. S. W. Borrero, Vollmer,
behavior. For Dan, agreement was 91% for Borrero, & Bourret, 2005; J. C. Borrero &
access to tangible items (range, 82% to 99%) Vollmer, 2002). If the functional analyses
and 96% for problem behavior (range, 86% to showed that problem behavior was sensitive to
100%). For Todd, agreement was 99% for multiple sources of reinforcement (e.g., atten-
access to tangible items (range, 98% to 100%) tion and tangible items), provision of either
and 95% for problem behavior (range, 91% to attention or tangible items was scored as
98%). For Walsh, agreement was 97% for
areinforcer.Onlyoneeventhadtobedelivered
attention (range, 93% to 100%), 93% for
within 10 s to be scored as a reinforced
escape from instructional demands (range,
response. For example, if 20 instances of
91% to 95%), 98% for access to tangible
problem behavior were observed and 10 of the
items, and 97% for problem behavior (range,
20 responses were reinforced (as previously
93% to 100%). For Antoine, agreement was
defined), the unit price (responses per re-
92% for access to tangible items (range, 76%
inforcer) was 2. Having determined the unit
to 100%) and 96% for problem behavior
price, we plotted consumption (demand func-
(range, 72% to 100%). Interobserver agree-
tions) and spending (work functions) at each
ment was assessed during 50% of all functional
unit price.
analysis sessions. Interobserver agreement for
Finally, we also calculated a single unit price
problem behavior exceeded 80% for all
value for each participant using the entire
participants.
descriptive observation. For example, if the
entire descriptive observation for 1 participant
Data Preparation (Descriptive Analysis)
was 2.5 hr, we calculated the unit price for the
Descriptive data were partitioned into three
entire 2.5 hr of descriptive observation and
equal intervals. For example, if the entire
plottedthetotalnumberofreinforcersobtained
descriptive observation was 3 hr in duration,
and total number of responses emitted at each
eachdatapointrepresented1 hrofobservation.
Data were also examined in 10- and 30-min unit price value. In this way, we were able to
increments. However, results were more vari- evaluate a larger rangeof unit price values. This
able when evaluated in 10- and 30-min method of analysis was designed to be analo-
increments (i.e., consumption was not well gous to that used by J. C. Borrero and Vollmer
described by changes in unit price). Unit price (2002) in evaluations of matching relations in
values were determined individually for each the natural environment.
UNIT PRICE AND SEVERE PROBLEM BEHAVIOR 469
RESULTS Table 1
Functional Analysis Resultsfor All Participants
Table 1 provides a summary of the assess-
ment findings, for all participants; however, Participant Results
note that functional analysis results for Mandy,
Mandy Attentionandtangibleitems
Dan, Todd, Walsh, and Antoine were reported Bruno Tangibleitemsandescape
Dan Tangibleitems
in prior work (see Footnote 1). Functional
Todd Edibleitems
analysis results for all participants showed that Walsh Attention,tangibleitems,andescape
the problem behavior of each participant was Antoine Tangibleitems
sensitive to socially mediated events as re-
values, the limited number of data points, or
inforcement.
both.
Figure 1 depicts the results of the demand
In addition to evaluating consumption and
functions and work functions for Mandy,
spending for 3 individual participants, overall
Bruno, and Dan on double logarithmic co-
consumption and spending were also evaluated
ordinates. Double logarithmic coordinates were
when the entire descriptive observation was
used in keeping with prior experimental
considered as a single observation. This yielded
behavioral economic research and because
a single unit price and a single work and
differences between consumption and spending
demand function. Each data point in Figure 2
at different unit price values are accentuated on
represents data for 1 participant on double
doublelogarithmicaxes(comparedtoarithmet-
logarithmiccoordinates.Whenevaluatedinthis
ic axes). For 3 participants (Todd, Walsh, and
way, the same monotonically decreasing func-
Alfonzo), reinforcers were not delivered during
tion was obtained for consumption and spend-
oneofthethreesegmentedintervals.Thus,data
ing. A rather minimal increase in spending was
for these participants are not included in
observed between the two leftmost data points
Figure 1. Overall, consumption and spending
(right panel), which arguably approximates the
decreased as a function of increasing unit price
bitonic function frequently reported in the
(producingmonotonicallydecreasingfunctions,
experimental literature. However, the global
or functions that move in only one direction as
shape of the function is monotonically de-
unit price increases). We also calculated the
creasing.
slope for each change in unit price. In this way,
changes in the slope of the function could be
DISCUSSION
interpreted in terms of demand elasticity.
Results for all participants demonstrated elastic The concept of unit price was extended to
demand (all had a slope with absolute value severe problem behavior exhibited by 6 indi-
greaterthan21),butfor2participants(Mandy viduals with developmental disabilities. De-
and Dan) the largest decrease in consumption scriptive observations provided the data neces-
occurred between transitions from Unit Price 1 sary to evaluate unit price under natural
to Unit Price 2. Results for Bruno produced environmental conditions that met the general
a steeper slope during transitions from Unit criteriaofadescriptiveanalysis(Bijou,Peterson,
Price 2 to Unit Price 3. This finding replicates & Ault, 1968; Iwata, Kahng, Wallace, &
prior experimental work; however, the func- Lindberg, 2000). Reinforcers were then empir-
tions obtained for response output did not ically determined by way of functional analysis,
produce the bitonic function that would have and descriptive data were then retrospectively
beenexpectedbasedonpriorexperimentalwork evaluated using the economic conceptualization
(e.g.,Maddenetal.,2000).Thismayhavebeen of unit price. Results of individual participant
a result of the rather limited range of unit price data and the group analysis showeddecreases in
470 JOHN C. BORRERO et al.
Figure1. Demandfunctions(left)andworkfunctions(right)forMandy,Bruno,andDaninlogarithmiccoordinates.
overall consumption as a function of increasing behavior exhibited by individuals with develop-
price. mental disabilities, under naturally occurring
The present study adds to the existing environmental conditions. However, the find-
behavioral economic literature by extending ing that demand was completely elastic, and
the concept of unit price to severe problem thus resulted in monotonic response output
UNIT PRICE AND SEVERE PROBLEM BEHAVIOR 471
Figure2. Demandfunctions(left)andworkfunctions(right)forallparticipants.Eachdatapointrepresentsdatafor
asingleparticipant,inlogarithmiccoordinates.Inbothpanels,thedatapointsrepresent(fromlefttoright)Dan,Mandy,
Bruno,Todd, Walsh, andAntoine.
curves, warrants some consideration. The curve. Notably, this was not observed in the
typical outcome of such analyses in traditional present study. Response curves were not
laboratory evaluations in the behavioral eco- bitonic, and there was no inelastic portion on
nomic literature is considerably different. As theleftofthedemandcurve.Clinically,thiscan
noted previously, demand is typically inelastic be viewed as a preferred outcome because at
on the left side of the demand curve, and even the lowest unit price values in the present
correspondingly, the response output curve is study, problem behavior decreased with in-
bitonic with increases in response output creasingprice.Perhapsiflowerunitpricevalues
initially followed by a decrease in response had been observed in the present study, an
output. In terms of the present study, as inelastic portion of the demand curve and
reinforcers were provided less frequently for bitonicresponseoutputfunctionmayhavebeen
problembehavior,problembehaviorcouldhave apparent. If that were the case, then problem
increased to maintain the same level of re- behavior may have initially increased with
inforcement. Returning to the tomato example, increasing unit price. Future research might
if the price of tomatoes were to increase from involve evaluations of conditions under which
$1.00perkilogramto$3.00perkilogram,total abitonicfunctionwouldbeapparent.Thismay
money spent (response output) could increase representanimportantclinicalsituation,similar
even if demand (tomatoes purchased) declines to an extinction burst, in which attempts at
slightly. That is, if 10 kg of tomatoes are eliminating problem behavior are initially met
purchasedat$2.00perkilogram,totalspending with increases in problem behavior.
is $20.00. But if only 8 kg are purchased at Economic concepts such as the simple
$3.00 per kilogram, total spending is $24.00. formulation of unit price used in the current
This is in the inelastic portion of the demand investigation,aswellasmorecomplexiterations
curve and is represented by the ascending limb involving response effort (e.g., Hursh et al.,
of a bitonic response output curve. At further 1988) and delay (e.g., Madden et al., 2000),
increases in price, response output may eventu- represent examples of quantitative models.
allydecline(e.g.,at$4.00perkilogram,perhaps Quantitative modeling encourages descriptions
only 4 kg are consumed, and total spending is of behavior that are precise and succinct while
$16.00). This represents the elastic portion of capturing relevant features of the phenomenon
the demand curve, and is represented by the under investigation (Shull, 1991). In recent
descending limb of a bitonic response output years,therehasbeenarevitalizedinterestinone
472 JOHN C. BORRERO et al.
particular quantitative model of behavior in the way in which unit price is manipulated (manip-
context of naturally occurring interactions: the ulations of amount while holding response
matching law (e.g., Oliver, Hall, & Nixon, requirement constant, manipulations of response
1999).Recentworkhasshownthatthematching requirement while holding amount constant, or
law(initsvariousiterations)effectivelydescribes proportional increases of both amount and
the allocation of problem and appropriate response requirement) may produce differential
behavior based on relative reinforcement rates. effects on response output. Therefore, future
The current investigation adds to the existing researchmayalsobedesignedtoassesstheeffects
literature on quantitative modeling by demon- ofexperimentalmanipulationsofunitpricebased
strating that problem behavior exhibited by on values obtained from descriptive data while
individuals with developmental disabilities re- arranging a range of absolute values that de-
plicates some features of the behavior of termineaunitprice.Forexample,ifaunitpriceof
consumers in laboratory contexts under increas- 9 were obtained via descriptive observations, an
ing price requirements. However, the current experimental arrangement of the same unit price
investigation is not without its limitations. could be arranged by provision of one reinforcer
First,weevaluatedconsumptionandspending for every nine responses or five reinforcers for
under a rather limited range of unit price values every 45 responses. Such evaluations would also
(threefor3participants,onefortheremaining3 extend the applicability of unit price and provide
participants).Theexperimentalliteratureonunit a larger amount of data for consideration.
price typically involves many more unit price A second limitation is that only one re-
values and repeated measures of behavior under inforcement parameter (frequency) was evalu-
eachvalue.Inadditiontotheanalysesreportedin ated. Other factors, such as the duration or
the present study, we also evaluated the de- magnitudeofreinforcementlikelycontributeto
scriptive data in smaller intervals (e.g., 10 min overall consumption. For example, if each
and 30 min). Results of those analyses did not instance of SIB produces one reinforcer (unit
produce orderly data, and it was not until price 5 1) but instances of a particularly high
descriptivedatawerepartitionedintoequalthirds intensity produce a larger duration of reinforce-
that any semblance of order was obtained. ment, price may likely be determined by
However, the finding that consumption and response effort (associated with self-injury),
spendingdecreasedgivenincreasesinpriceacross reinforcer frequency, and reinforcer magnitude.
such a small range of unit price values speaks to Future research may be specifically designed to
thegeneralityofunitpriceasausefulconceptin
evaluate multiple parameters of reinforcement
applied behavior analysis.
in determining price, because prior descriptive
Future research may be designed to arrange
research has shown that reinforcement param-
unit prices experimentally, based on those
eters may influence overall response output (C.
values derived from descriptive observations as
S. W. Borrero et al., 2005).
well as additional unit price values. For
Third, the method of assessing consumption
example, if analyses from descriptive observa- in the present study is consistent with classical
tionsproduceresponsestoreinforcerratiosof3, economic conceptualizations (there was no
6, and 9 (across an extended observation experimental manipulation of price). However,
period), experimentally arranged unit price the elaborate covariate models used in econo-
valuesthatmimicthoseobtainedviadescriptive metrics were not employed to statistically
observations may provide a stronger demon- control for confounding factors (e.g., settings,
stration of the utility of the model. The recent alternative reinforcement and activities). Were
work of Madden et al. (2000) suggests that the such statistical control procedures employed,